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A282757
2*n analog to Keith numbers.
13
5, 9, 10, 15, 19, 20, 25, 28, 30, 35, 40, 45, 47, 66, 88, 132, 198, 2006, 2740, 4012, 4419, 13635, 56357, 338540, 354164, 419966, 441972, 685704, 803678, 1528803, 1844810, 9127005, 12305952, 14315686, 14650155, 15828353, 17838087, 22618003, 37826729, 71644613
OFFSET
1,1
COMMENTS
Like Keith numbers but starting from 2*n digits to reach n.
Consider the digits of 2*n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
EXAMPLE
2*28 = 56 :
5 + 6 = 11;
6 + 11 = 17;
11 + 17 = 28.
MAPLE
with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000, 2);
MATHEMATICA
Select[Range[10^6], Function[n, Module[{d = IntegerDigits[2 n], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)
CROSSREFS
Sequence in context: A272902 A235033 A327593 * A199718 A155470 A266399
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 22 2017
STATUS
approved